Inference for Moment Inequalities: A Constrained Moment Selection Procedure

TL;DR

This paper introduces a modified generalized moment selection (GMS) testing procedure for models with moment inequalities, enhancing finite-sample performance and local power while remaining computationally feasible.

Contribution

It develops a tilting method for GMS tests that improves power and size control in finite samples, especially with many moment inequalities.

Findings

Modified GMS tests control size well.

Enhanced local power over non-modified tests.

Computational feasibility with many inequalities.

Abstract

Inference in models where the parameter is defined by moment inequalities is of interest in many areas of economics. This paper develops a new method for improving the performance of generalized moment selection (GMS) testing procedures in finite-samples. The method modifies GMS tests by tilting the empirical distribution in its moment selection step by an amount that maximizes the empirical likelihood subject to the restrictions of the null hypothesis. We characterize sets of population distributions on which a modified GMS test is (i) asymptotically equivalent to its non-modified version to first-order, and (ii) superior to its non-modified version according to local power when the sample size is large enough. An important feature of the proposed modification is that it remains computationally feasible even when the number of moment inequalities is large. We report simulation results that show the modified tests control size well, and have markedly improved local power over their non-modified counterparts.